Final answer:
To find the least integer n such that f(x) is o(x^n), we need to consider the growth rate of f(x). For a constant function like f(x) = 20 within a restricted domain, f(x) grows slower than any positive power of x, and thus n would be at least 1. We must remember that a smaller growth rate of f(x) correlates with a larger n.
Step-by-step explanation:
The student has asked to find the least integer n such that a function f(x) is o(xn), which is a question from the field of asymptotic analysis in mathematics. To identify the least integer n, we need to understand the growth rate of the given function. The notation o(xn) means that f(x) grows at a slower rate than xn as x approaches infinity.
Discussing a specific function, let's consider if f(x) is a constant function, such as f(x) = 20 for 0 ≤ x ≤ 20. This function is a horizontal line and thus grows slower than any positive power of x. We would select n = 1 because a constant function grows slower than any xn for any n > 0.
It's important to recall that as the number N decreases in magnitude, the exponent increases and vice versa. So, if we are given a function with a smaller growth rate, we would look for a larger n to satisfy the condition that f(x) is o(xn).